# Stored data for newform 105.2.g.a, downloaded from the LMFDB on 19 April 2024.
{"label": "105.2.g.a", "space_label": "105.2.g", "level": 105, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 412350414953, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2304.1", "trace_hash": 2177582815243144749, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-3, 0, 1]], [13, [4, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(-1-\\beta _{1})q^{3}+q^{4}+(\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 105, "char_orbit_label": "g", "char_is_real": true, "Nk2": 420, "analytic_conductor": 0.838429221223444, "hecke_ring_index": 2, "level_radical": 105, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.762", "prec": 17}, "analytic_rank_proved": true, "char_values": [105, 2, [71, 22, 31], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 5, 7], "conrey_indexes": [104], "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [1, 0, 4, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.006", "prec": 17}, {"__RealLiteral__": 0, "data": "3.597", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "113.843", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4499.600", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -4, 0, 4], "traces": [0, 4, 0, -4, 4, 0, 0, 4, 0, -4, 12, 0, -4, -16, 0, 8, -20, 0, 0, 0, 0, -4, 0, 0, 0, 4, 0, 20, 4, 0, -12, 0, 0, 16, 0, 0, -4, 0, 0, 16, -12, 0, -24, 0, 0, -16, 24, 0, 20, -20, 0, 16, -16, 0, 0, -16, 0, 0, 0, 0, 8, 0, 0, -4, 4, 0, 0, 0, 0, 0, 36, 0, 0, 32, 0, -4, 0, 0, 0, 32, 0, -28, 24, 0, -4, -16, 0, -32, 0, 0, -12, -16, 0, 0, 0, 0, 0, 32, 0, -32, 4, 0, 0, -40, 0, -16, 0, 0, 20, -40, 0, 0, -20, 0, 0, 24, 0, 16, -48, 0, 12, 12, 0, 0, 0, 0, 48, 0, 0, 0, -48, 0, 16, 0, 0, 8, 0, 0, -24, 0, 0, 16, 0, 0, 20, 32, 0, 20, 0, 0, 48, 32, 0, -32, 48, 0, 16, -16, 0, 0, -36, 0, 0, 0, 0, 16, 0, 0, 24, 12, 0, 0, 0, 0, 0, 52, 0, 0, -72, 0, -16, 0, 0, 0, -24, 0, -96, -32, 0, 20, 0, 0, -4, 0, 0, -32, -20, 0, 0, 0, 0, 0, 120, 0, 16, 24, 0, 0, 80, 0, -36, -16, 0, 16, -72, 0, 0, -96, 0, -32, -16, 0, 0, 104, 0, -4, -48, 0, 0, 0, 0, 16, 0, 0, 0, -16, 0, -32, 48, 0, -40, 0, 0, -4, 0, 0, -24, 0, 0, 16, -36, 0, -4, 0, 0, 16, 76, 0, -48, 0, 0, 64, -48, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 16, 48, 0, 0, 0, 0, 0, -36, 0, 0, 56, 0, 0, 0, 0, 0, 36, 0, -32, 32, 0, -48, -48, 0, 16, 0, 0, -4, -48, 0, 0, 0, 0, 0, -40, 0, 40, 96, 0, 0, -64, 0, 32, 32, 0, 0, 64, 0, 0, 24, 0, -28, -16, 0, 40, -24, 0, 48, -112, 0, 0, 0, 0, 20, 0, 0, 0, -16, 0, 0, -68, 0, -24, 0, 0, -32, 0, 0, -80, 0, 0, 48, -16, 0, 16, 0, 0, 12, 76, 0, -12, -16, 0, 96, -40, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, -24, -112, 0, 0, 0, 0, 0, 32, 0, 0, 32, 0, 48, 0, 0, 0, 0, 0, -32, 80, 0, 0, -20, 0, 48, 0, 0, 32, -96, 0, 0, 0, 0, 0, -40, 0, -24, -16, 0, 0, 0, 0, -16, 104, 0, -32, 0, 0, 0, 96, 0, -64, 48, 0, -100, -64, 0, -32, -40, 0, 0, 0, 0, 20, 0, 0, 0, -72, 0, 64, 4, 0, -96, 0, 0, -32, 0, 0, 0, 0, 0, 16, 24, 0, -48, 0, 0, -96, 144, 0, 16, 48, 0, 16, 48, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, -48, 12, 0, 0, 0, 0, 0, -12, 0, 0, 64, 0, 16, 0, 0, 0, -16, 0, -80, -144, 0, -48, 120, 0, -12, 0, 0, 48, 32, 0, 0, 0, 0, 0, -32, 0, 112, 48, 0, 0, 104, 0, -52, -24, 0, -80, -44, 0, 0, 0, 0, 72, -72, 0, 16, 72, 0, 8, -40, 0, 0, 0, 0, 96, 0, 0, 0, -96, 0, 24, 32, 0, 0, 0, 0, 192, 0, 0, 32, 0, 0, 16, -48, 0, -28, 0, 0, 0, -16, 0, 112, 24, 0, -4, 32, 0, 0, 32, 0, 0, 0, 0, 64, 0, 0, 20, 0, 0, 0, 0, 0, 0, 32, 0, 0, -96, 0, -48, 0, 0, 0, 32, 0, -120, -40, 0, -32, -96, 0, -32, 0, 0, -24, -48, 0, 0, 0, 0, 0, -192, 0, -80, -92, 0, 0, -16, 0, -36, 32, 0, 16, -96, 0, 0, 80, 0, -32, 84, 0, 72, -88, 0, -48, 0, 0, 0, 0, 0, 96, 0, 0, 0, -48, 0, -32, 48, 0, 16, 0, 0, -64, 0, 0, 0, 0, 0, -104, -48, 0, 72, 0, 0, 20, 12, 0, 48, 32, 0, 16, 192, 0, 0, 48, 0, 0, 0, 0, 48, 0, 0, -32, -120, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 16, 0, 0, 0, 152, 0, -32, 72, 0, -48, 64, 0, 16, 0, 0, 80, -40, 0, 0, 0, 0, 0, -40, 0, 92, 96, 0, 0, -112, 0, -88, -72, 0, -24, 80, 0, 0, 0, 0, 96, -64, 0, -32, -32, 0, 36, 32, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -144, -40, 0, 16, 0, 0, -76, 0, 0, -80, 0, 0, 96, 192, 0, 0, 0, 0, -32, -32, 0, -32, 100, 0, 48, 56, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 72, 0, 0, -120, 0, -84, 0, 0, 0, 0, 0, -80, 0, 0, 16, 24, 0, -48, 0, 0, 16, -48, 0, 0, 0, 0, 0, -16, 0, -96, 80, 0, 0, -48, 0, 36, -12, 0, 160, -16, 0, 0, 12, 0, -56, -96, 0, 16, 80, 0, 0, 72, 0, 0, 0, 0, -48, 0, 0, 0, -112, 0, -36, -96, 0, -96, 0, 0, -32, 0, 0, -32, 0, 0, 16, 80, 0, 96, 0, 0, 48, 120, 0, 0, -144, 0, 64, 104, 0, 0, -16, 0, 0, 0, 0, -4, 0, 0, 48, 48, 0, 0, 0, 0, 0, -144, 0, 0, -32, 0, 96, 0, 0, 0, -64, 0, 40, -24, 0, 16, 0, 0, 40, 0, 0, -96, 0, 0, 0, 0, 0, 0, 32, 0, 64, -16, 0, 0, 48, 0, -16, 96, 0, -32, -128, 0, 0, -48, 0, 0, -112, 0, -64, 192, 0, 8, -260, 0, 0, 0, 0, -24, 0, 0, 0, 96, 0, -4, -96, 0, 16, 0, 0, 144, 0, 0, 40, 0, 0, 24, 0, 0, 16, 0, 0, -96, 32, 0, 112, 48, 0, 16, -208, 0, 0, 36], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 35, 3, -1, 2, 0], [1, 1, 105, 7, 1, 2, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "105.2.g.a", "char_is_minimal": true, "conrey_index": 104, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [-1, -1, 0, 0], [1, 0, 0, 0], [0, 1, -1, 0], [0, 0, 1, 1], [1, 0, 0, 1], [0, 0, 1, 0], [-1, 2, 0, 0], [3, 0, 0, -1], [0, 2, 0, 0], [-1, -1, 0, 0], [-4, 0, 0, 0], [0, -3, -1, 0], [2, -1, 1, 1], [-5, 0, 0, 0], [0, 2, 0, 0], [0, 0, 1, -2], [0, 0, 0, 0], [0, 1, -1, 0], [-1, -1, 2, -1], [0, 0, 0, -2], [0, 0, -2, 0], [0, 0, -1, -1], [1, 0, 0, -2], [0, 0, 4, 0], [5, -1, 0, 0], [1, 0, 0, 1], [0, -4, 0, 0], [-3, -3, -2, 1], [0, 0, 0, 4], [0, 0, 3, 0], [4, -2, 0, 0], [0, 0, 0, -2], [0, -2, -3, 0], [-1, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [4, 4, 0, 0], [-3, 0, 0, 1], [0, 0, -2, 0], [-6, 3, 1, 1], [0, 0, 0, 2], [0, 2, 0, 0], [-4, -1, 1, -2], [6, 0, 0, 0], [0, 2, 0, 0], [5, 5, 0, 0], [-5, 0, 0, 2], [0, 6, -1, 0], [4, -2, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, -5, 1], [-4, 0, 0, -2], [0, 3, 1, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 4, 0], [2, -1, 1, 1], [0, 0, 0, -4], [0, -12, 0, 0], [-1, 2, -4, -1], [1, 0, 0, 0], [0, -4, 4, 0], [0, 0, -4, 2], [0, 0, 0, -2], [0, 2, 0, 0], [0, 0, 2, 2], [9, 0, 0, 2], [0, 2, 0, 0], [0, 0, -1, 2], [8, 0, 0, 0], [0, 0, 0, 0], [-1, -1, -4, 2], [0, 0, 0, 0], [0, 2, -4, 0], [0, 0, -4, -4], [8, 0, 0, 0], [0, -5, 5, 0], [-7, -4, 0, 0], [6, 0, 0, 0], [0, 2, 0, 0], [-1, -1, 2, -1], [-4, 0, 0, -2], [0, -6, 0, 0], [-8, 4, 0, 0], [0, 0, 0, 2], [0, 0, 6, 0], [-3, 6, 4, 1], [-4, 0, 0, -4], [0, 0, -2, 0], [0, 0, 8, -4], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -3, -3], [8, 0, 0, 0], [0, -6, 5, 0], [-8, -2, 0, 0], [1, 0, 0, -2]]}